It was my good fortune to have been a graduate student in statistics at U. C. Berkeley when David Blackwell joined the faculty there in 1954. The distinguished statisticians who were there already —, , , , , and others — constituted the most approachable faculty I’ve seen anywhere. We students shared coffee and conversation with them in the afternoons. When Blackwell joined the group, he fit right in with his warm humor, his winning smile, his modesty and his congeniality with the students.
He had an outstanding mathematical reputation by that time, having been invited to give an address in probability at the ICM meetings in Amsterdam in 1954. In 1955 he was elected president of the Institute of Mathematical Statistics. Important for me personally was his book with, Theory of Games and Statistical Decisions, which came out in 1954. At that time, I was working on my thesis under the direction of Lucien Le Cam. I took a course from Blackwell and read his book, which views statistics as a subset of the art of making decisions under uncertainty. The beauty of this view influenced me to such an extent that my subsequent work did not go so much in the direction of the topics of my thesis but more in the direction of the areas that interested Blackwell — game theory, probability, and sequential decisions.
Dave was one of the early Bayesian statisticians, that is, he considered statistics, and life as well, as a process of observation, experiment, information gathering, and, based on one’s prior beliefs and the outcomes of the observations, modifying one’s opinions and acting accordingly. Although his views certainly influenced me, I was never a complete Bayesian — no student of Le Cam could be — but of all the Bayesians I know, he was the most persuasive. It was characteristic of him to spread his interests over several areas rather than to specialize in one. It is amazing how he managed to produce deep and original results in several fields. The underlying theme of his work springs from his Bayesian perspective: probabilistic, sequential decision making and optimization.
Let me mention just a few of his achievements. In probability, there is a basic renewal theorem that goes by his name. There is his work in Markov decision processes in which he conceived the concepts of positive and negative dynamic programs and in which the notion of Blackwell optimality plays an important role.
In statistics, there is the famous–Blackwell theorem and its association with a simple method of improving estimates now called Rao–Blackwellization. There is a fundamental paper of , Blackwell, and that helped lay the foundation for Bayesian sequential analysis. The subject of comparison of experiments was introduced by Blackwell and in 1952. The notion of merging of opinions with increasing information was introduced by Blackwell and in 1962.
In game theory, he has initialized several areas: games of timing, starting with Rand reports on duels; games of attrition; the vector-valued minimax theorem, leading to the notions of approachability and excludability, etc. He has had a long interest in set theory and analytic sets. This led to his study of conditions under which certain infinitely long games of imperfect information have values. This has had a deep impact in the field of logic; logicians now call such games Blackwell games.
My own professional interaction with him came in 1967–1968. He suggested working on a problem in the area of stochastic games. In 1958had given an example of a stochastic game that did not have a value under limiting average payoff if the players are restricted to using stationary strategies. Dave called this example game the “Big Match”. He wondered if the game had a value if all strategies were allowed. After working on the problem together for a while, we simultaneously and independently came up with different proofs of the existence of a value. To me, it was just an interesting problem. But Dave somehow knew that the problem was important. It was the first step in showing that all stochastic games under limiting average payoff have a value. This took another fourteen years, with many scholars contributing partial results before the result was finally completely proved.
Dave Blackwell is one of my role models. He influenced me in my professional work and in my personal life. He was a great teacher, both in the classroom and in conversations on general subjects. He had a way of cutting through massive detail to get to the heart of a problem. He had over sixty Ph.D. students. But if you count people like me, he had many more students. His spirit and his works are still alive in all of us.